Ashley Stain, 21, from the Isle of Wight, made the pledge just hours before England played Wales in a friendly on Thursday night.
Ashley, originally from Walsall, said he was "absolutely shocked" when Coady scored on 53 minutes - the 27-year-old's first goal in two years - and had forgotten about his tweet.
But the life-long Wolves fan plans to fully honour his pledge and get the tattoo next Friday. A company called Heritage Improvement has offered to pay the costs.
Ashley told the Express & Star: "Coady as a player and person is an absolute legend. He is by far my favourite player and seems the most humble man ever.
"I didn't expect Coady to score being as it's been so long. It was just an absolute shock when he did. I forgot about the tweet until after he scored.
"I'm getting the tattoo done next Friday after a business called Heritage Improvements offered to pay for the full tattoo, and a local tattooist had a slot."
Ashley's tweet has since gone viral which has received more than 1,400 retweets and 17,500 likes.
Fellow Twitter users were quick to show their appreciation for Ashley's gesture, with Tim Gollins tweeting: "Cant wait to see the finished tattoo, I think Wolves should let you come and show Coady the tattoo once finished."
Ashley plans to have the tattoo of Coady's face on the back of his left leg. He already has some ink of a "wolf over a moon" on his left arm.
Ashley has been a Wolves fan all his life and says he has "never looked back" on supporting his boyhood club.
And despite living 180 miles from Molineux, Ashley says he still "gets to many games" where possible.